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George Pirlea
Iris
Commits
5f13409c
Commit
5f13409c
authored
Dec 14, 2015
by
Robbert Krebbers
Browse files
Some more namespace lemmas.
parent
6e9a9572
Changes
1
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Inline
Side-by-side
iris/namespace.v
View file @
5f13409c
...
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@@ -8,15 +8,19 @@ Definition nclose (I : namespace) : coPset := coPset_suffixes (encode I).
Instance
ndot_injective
`
{
Countable
A
}
:
Injective2
(=)
(=)
(=)
(@
ndot
A
_
_
).
Proof
.
by
intros
I1
x1
I2
x2
?
;
simplify_equality
.
Qed
.
Definition
nclose_nnil
:
nclose
nnil
=
coPset_all
.
Lemma
nclose_nnil
:
nclose
nnil
=
coPset_all
.
Proof
.
by
apply
(
sig_eq_pi
_
).
Qed
.
Definition
nclose_subseteq
`
{
Countable
A
}
I
x
:
nclose
(
ndot
I
x
)
⊆
nclose
I
.
Lemma
encode_nclose
I
:
encode
I
∈
nclose
I
.
Proof
.
by
apply
elem_coPset_suffixes
;
exists
xH
;
rewrite
(
left_id_L
_
_
).
Qed
.
Lemma
nclose_subseteq
`
{
Countable
A
}
I
x
:
nclose
(
ndot
I
x
)
⊆
nclose
I
.
Proof
.
intros
p
;
unfold
nclose
;
rewrite
!
elem_coPset_suffixes
;
intros
[
q
->].
destruct
(
list_encode_suffix
I
(
ndot
I
x
))
as
[
q'
?]
;
[
by
exists
[
encode
x
]|].
by
exists
(
q
++
q'
)%
positive
;
rewrite
<-(
associative_L
_
)
;
f_equal
.
Qed
.
Definition
nclose_disjoint
`
{
Countable
A
}
I
(
x
y
:
A
)
:
Lemma
ndot_nclose
`
{
Countable
A
}
I
x
:
encode
(
ndot
I
x
)
∈
nclose
I
.
Proof
.
apply
nclose_subseteq
with
x
,
encode_nclose
.
Qed
.
Lemma
nclose_disjoint
`
{
Countable
A
}
I
(
x
y
:
A
)
:
x
≠
y
→
nclose
(
ndot
I
x
)
∩
nclose
(
ndot
I
y
)
=
∅
.
Proof
.
intros
Hxy
;
apply
elem_of_equiv_empty_L
;
intros
p
;
unfold
nclose
,
ndot
.
...
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